Problem: Simplify the following expression: $k = \dfrac{20fg - 50g^2}{40g^2 + 30hg} + \dfrac{40hg - 20g^2}{40g^2 + 30hg}$ You can assume $f,g,h \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{20fg - 50g^2 + 40hg - 20g^2}{40g^2 + 30hg}$ $k = \dfrac{20fg - 70g^2 + 40hg}{40g^2 + 30hg}$ The numerator and denominator have a common factor of $10g$, so we can simplify $k = \dfrac{2f - 7g + 4h}{4g + 3h}$